Popper (1972, 107-108) presents one of his “standard arguments for the independent existence of the third world” with the help of a thought experiment. Compare the following two situations: (a) All our machines and tools are destroyed, and all our knowledge of them. But books and our capacity to learn from them survive; and (b) all our machines and tools are destroyed, and all our knowledge of them. All books are destroyed, too.
In the second case, Popper argues, it would take much more time for the world to reemerge. I think that this hypothesis is quite plausible. Let us assume it is true. What follows from this? According to Popper (1972, 108), his thought experiment demonstrates the “reality, significance, and degree of autonomy of the third world.”
This, however, does not follow from the premises of the thought experiment. Strictly speaking, this thought experiment only demonstrates the significance of books. We may conclude that books, at least some of them, are significant things, which could, under special conditions, decisively influence how the world goes on. If we presuppose, in addition, that books are world 3 objects, then it follows that some world 3 objects are significant things. But the thought experiment itself does not tell us that there is a world 3, and that books are world 3 objects. Books could have great impact yet be physical things. After all, physical things can also significantly change the world, and our life (e.g., the impact of a meteorite).
Popper further illustrates the reality and influence of world 3 by referring to problem situations in science and mathematics. As an example, he presents Brouwer’s invention of his theory of the continuum. He cites the following statement by Heyting about Brouwer’s invention: “If recursive functions had been invented before, Brouwer would perhaps not have formed the notion of a choice sequence” (Popper 1972, 109).
The details of this example do not matter. The example illustrates the point in question. Quite plausibly, problem situations may greatly influence the thinking of scientists. But here, too, we have to distinguish between two questions. The first is whether problem situations exert an influence on world 2, and perhaps on world 1. It is quite another question what problem situations are ontologically. They might be world 3 objects, but they might also belong to worlds 1 or 2. Popper’s example teaches us nothing about this question. It only illustrates the impact of problem situations, not their ontological character.